For tertiary English as a Foreign Language (EFL) students, academic writing is not an easy task. It requires knowledge of the academic writing genres with their particular linguistic features. Moreover, academic writing demands good critical thinking. This research aims to explore the students' academic writing competencies that also focus on critical thinking. The research involved thirty-six first-year tertiary EFL students from a regular class of a private university in Pontianak, West Kalimantan, Indonesia. The source for data collection was the students’ texts. Three texts were selected and the students were categorized into low, medium, and high levels of writing achievement. The text analysis utilized functional grammar rooted in systemic functional linguistics (Emilia, 2014). The analysis shows that the students, regardless of their levels of writing achievement, have little control over the schematic structure and linguistic features of an argumentative writing. The text analysis also shows that the students’ texts have some limitations as regards their critical thinking capacity. Still, a few examples of academic language were detected in the texts. The findings suggest that the lecturer should incorporate explicit teaching and cooperative learning activities to alleviate the students' difficulties and develop their academic writing and critical thinking capacity.